Question
A 2 kg cart moving right at 3 m/s sticks to a stationary 1 kg cart. External horizontal impulse is negligible. What is their velocity immediately after the collision?
- a.1 m/s right
- b.2 m/s right
- c.3 m/s right
- d.About 2.45 m/s right
Correct answer
B. 2 m/s right
Full reasoning
- 1Choose both carts together as the system; their contact forces are internal.
- 2The initial momentum is (2)(3) + (1)(0) = 6 kg m/s to the right.
- 3The combined mass is 3 kg, so the final velocity is 6/3 = 2 m/s to the right.
- 4Initial kinetic energy is 9 J; final kinetic energy is 6 J. The 3 J difference becomes other forms of energy. Momentum conservation does not require kinetic energy conservation.
Why each choice is right or wrong
Choice A
This does not preserve the initial total momentum of 6 kg m/s.
Choice B
Correct. The final 3 kg mass carries the initial momentum of 6 kg m/s.
Choice C
This preserves the first cart’s speed but not the two-cart momentum: 3 kg at 3 m/s would carry 9 kg m/s rather than 6.
Choice D
This comes from conserving kinetic energy, which a sticking collision does not conserve.
Related formula
Momentum conservation for two sticking carts
m1 v1 + m2 v2 = (m1 + m2) vf
Assumptions: The carts stick together and the external impulse along the chosen axis is negligible.
Related topic and practice
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Sources
Original authored exercise; no database question ID and no protected or official exam-bank content. Specialist review pending.
- University Physics Volume 1, Section 9.3: Conservation of Linear Momentum — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.
Sources and corrections
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